From a matrix, Pick one element from each row and not from same column for all possibilities. Only for non zero elements.

Question

MeMariah 2020-7-8

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https://ww2.mathworks.cn/matlabcentral/answers/561602-from-a-matrix-pick-one-element-from-each-row-and-not-from-same-column-for-all-possibilities-only-f

评论： MeMariah 2020-9-20

采纳的回答： Puru Kathuria

Hi, From a matrix, I would like to pick one element from each row and not from same column for all possibilities.

Only for non zero elements.

Example, from A = [1 2 0; 1 2 0; 0 0 3], I want to obtain (1 2 3 and 2 1 3).

Thank you

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Answer 1

Puru Kathuria 2020-7-22

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Hi,

Your requirements are answered in a similar question mentioned in this link. Also, selecting set of elements from a matrix such that each element comes from distinct row and column can also be modeled as a Matching problem. (graph theory)

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MeMariah 2020-7-23

Thank you Puru Kathuria.

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Answer 2

Bruno Luong 2020-7-23

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https://ww2.mathworks.cn/matlabcentral/answers/561602-from-a-matrix-pick-one-element-from-each-row-and-not-from-same-column-for-all-possibilities-only-f#answer_469668

编辑：Bruno Luong 2020-7-23

在 MATLAB Online 中打开

A dynamic programming for fun

function p = nzperm(A,c)
if nargin < 2
    c = 1;
end
r = find(A(:,c));
if isempty(r)
    p = [];
elseif c==size(A,2)
    p = A(r,c); % p = r(:);
else
    p = [];
    for i=r.'
        Ai = A;
        Ai(i,:) = 0;
        q = nzperm(Ai,c+1);
        a = A(i,c); % a = i
        q = [a+zeros(size(q,1),1) q];
        p = [p; q]; %#ok
    end
end

Result

>> A=rand(5); A = A.*(rand(size(A))>0.6)
A =
         0    0.6468    0.7881    0.5598    0.8008
    0.5607         0         0         0    0.8961
         0         0         0    0.9394    0.5975
         0    0.4756    0.1335         0         0
         0    0.3625    0.0216         0    0.9437
>> nzperm(A)
ans =
    0.5607    0.6468    0.1335    0.9394    0.9437
    0.5607    0.4756    0.7881    0.9394    0.9437
    0.5607    0.4756    0.0216    0.5598    0.5975
    0.5607    0.4756    0.0216    0.9394    0.8008
    0.5607    0.3625    0.1335    0.5598    0.5975
    0.5607    0.3625    0.1335    0.9394    0.8008

Note: this code will be slow on large array, since MATLAB make copies of matrix at every step. This algorithm could be implemented without copy using C mex.

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MeMariah 2020-7-23

You are a genius, am so grateful.

MeMariah 2020-9-20

@Bruno, you are right. large array take long. Unfortunately, I keep getting error when I try to generate the C mex file. Am using this app for the first time. Are able to help? error points to the line with

for i= r.'

Thanks.

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